Obstructions for constructing equivariant fibrations

Güçlükan İlhan, Aslı¹

¹Department of Mathematics, Bilkent University, Ankara 06800, Turkey

Algebraic and Geometric Topology, Tome 12 (2012) no. 3, pp. 1313-1330

Résumé

Let G be a finite group and ℋ be a family of subgroups of G which is closed under conjugation and taking subgroups. Let B be a G–CW–complex whose isotropy subgroups are in ℋ and let ℱ = {FH}H∈ℋ be a compatible family of H–spaces. A G–fibration over B with the fiber type ℱ = {FH}H∈ℋ is a G–equivariant fibration p: E → B where p−1(b) is Gb–homotopy equivalent to FGb for each b ∈ B. In this paper, we develop an obstruction theory for constructing G–fibrations with the fiber type ℱ over a given G–CW–complex B. Constructing G–fibrations with a prescribed fiber type ℱ is an important step in the construction of free G–actions on finite CW–complexes which are homotopy equivalent to a product of spheres.

Détail

DOI : 10.2140/agt.2012.12.1313

Classification : 57S25, 55R91
Keywords: equivariant fibration, Bredon cohomology, obstruction theory, group action

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